/* US population                                */
 /* population in millions from decennial census */
 /*  (updated -- Table 16 1993)                  */
  options ls=80 ps=40 ;
  data a ; 
    input year pop ; 
    yryr = year * year ;      * square ;
    yrc = year - 1880 ;       * center ;
    yyrrcc = yrc*yrc ;        * square of centered x ;
 cards ;
   1790   3.929
   1800   5.308
   1810   7.240 
   1820   9.638
   1830  12.861
   1840  17.063
   1850  23.192
   1860  31.443
   1870  38.558
   1880  50.189
   1890  62.980
   1900  76.212
   1910  92.228
   1920 106.022
   1930 123.203
   1940 132.165
   1950 151.326
   1960 179.323
   1970 203.302
   1980    .
   1990    .
   2000    .
;
run ;
  proc plot data=a ;
    plot pop*year ;
    title 'US Population (Millions) from decennial census' ;
run ;
 /*          quadratic regression      */
  proc reg data=a ;
    model pop = year yryr / covb ;
    title 'quadratic regression' ;
run ;
 /* quadratic regression - centered x  */
  proc reg data=a ;
    model pop = yrc yyrrcc / covb ;
    title 'quadratic regression with centered variable' ;
run ;